He seems to have proven the following:
PROBLEM: Given a 6 vertex graph (via (6 choose 2) Boolean inputs) you want to determine if it has a triangle. If you want to build a circuit for this problem just using NAND gates, how many are required.
PARTIAL ANSWER: The problem requires at least 21 NAND gates. ((6 choose 3), plus one output gate; what you'd probably expect, in other words.)
He has asked me two questions that I toss out to the audience
- Is the result correct? (probably) Does it contradict anything known (I doubt that)? Does the proof seem correct? (I think so.)
- Is the result interesting? To me this is the more interesting question (or meta-question). Are results about actual concrete numbers interesting? My first answer is only if (1) they lead to more more general results, or (2) use interesting techniques. So the answer may be, using (1), I DON"T KNOW, and (2) may be subjective.